Geodesic
Maps to the projective plane
Dydak, Jerzy1 ; Levin, Michael2
1Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, United States
2Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel
Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 549-568
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We prove the projective plane ℝP2 is an absolute extensor of a finite-dimensional metrizable space X if and only if the cohomological dimension mod 2 of X does not exceed 1. This solves one of the remaining difficult problems (posed by A N Dranishnikov) in Extension Theory. One of the main tools is the computation of the fundamental group of the function space Map(ℝPn, ℝPn+1) (based at the inclusion) as being isomorphic to either ℤ4 or ℤ2 ⊕ ℤ2 for n ≥ 1. Double surgery and the above fact yield the proof.

DOI : 10.2140/agt.2009.9.549
Keywords: absolute extensor, cohomological dimension, covering dimension, extension dimension, extension of maps, projective space

Dydak, Jerzy  1   ; Levin, Michael  2

1 Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, United States
2 Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel 
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Dydak, Jerzy; Levin, Michael. Maps to the projective plane. Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 549-568. doi: 10.2140/agt.2009.9.549

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